where \(\sum _{e^{\prime }\ne  e}\)  sums over all edges different from \(e\) , \(\sum _{v_i<e^{\prime }}\)  over the nodes shared by \(e\)  and \(e^{\prime }\) , and \(f_e\)  denotes the faces containing \(e\) , so \(\sum _{f_e > e^{\prime }}\)  sums over all faces containing both \(e\)  and \(e^{\prime }\) . Once again, the formula greatly simplifies for unweighted networks (see Lemma 1 of [1]}):
